Prediction: The Future of the USA Stock Market

Based on a theory of cooperative herding and imitation working both in bullish
as well as in bearish regimes that we have developed in a series of papers,
we have detected the existence of a clear signature of herding in the decay
of the US S&P500 index since August 2000 with high statistical significance,
in the form of strong log-periodic components. Since August 2000, the USA as
well as most other western markets have depreciated almost in synchrony according
to complex patterns of drops and local rebounds. We have proposed to describe
this phenomenon using the concept of a log-periodic power law (LPPL) antibubble,
characterizing behavioural herding between investors leading to a competition
between positive and negative feedbacks in the pricing process. This work was
motivated by the similitude between the evolutions of Nikkei 225 and S&P
500 Index.

Fig. 1 shows 9 years of the evolution of the Japanese Nikkei index and almost
8 years of the USA S&P500 index, compared to each other after a translation
described in the update of September 17, 2003 has been performed. The years
are written on the horizontal axis (and marked by a tick on the axis where
January 1 of that year occurs). This figure illustrates an analogy noted by
several observers that our work has made quantitative. The oscillations with
decreasing frequency which decorate an overall decrease of the stock markets
are observed only in very special stock markets regimes, that we have terms
log-periodic "anti-bubbles". By analyzing the mathematical structure of these
oscillations, we quantify them into one (or several) mathematical formula(s)
that can then be extrapolated to provide the prediction shown in the following
figures. Note that extrapolating is often a risky endeavour and needs to be
justified. In our case, the extrapolations, which give the forecasts, are based
on the belief that these equations offered below embody the major forces in
the market at the macroscopic scale. This leads to the possibility of describing
several probable scenarios. We do not believe in the existence of deterministic
trajectories but we aim at targeting the most probable future paths.

Please refer to the following paper for a detailed description: D. Sornette
and W.-X. Zhou, The US 2000-2002 Market Descent: How Much Longer and Deeper?
Quantitative Finance 2 (6), 468-481 (2002) (e-print at http://arXiv.org/abs/cond-mat/0209065).

Why Stock Markets Crash: For a general presentation of the underlying concepts,
theory, empirical tests and concrete applications, with a discussion of previous
predictions, see the recent book, Why Stock Markets Crash.

Several of our readers have suggested to us that we should analyze the data
from the perspective of foreigners, by converting the market price in euro,
British pound or Yen, for instance. This makes sense if one takes into account
(1) the artificial and distorting input of the liquidity input by the Fed (which
amounts to an effective inflation in dollar terms, hence its depreciation,
to be naively simple) and (2) the importance of foreign investors on the US
stock markets recycling their surplus dollars. As the figures below show, the
picture from the vantage of a foreigner is very different than for an US investor.
The tentative conclusion of this new study is that the strong impact of the
Fed intervention has perturbed the fingerprints of the antibubble, so that
we conclude that it has ended in the US, while maybe in reality the herding
bearish-bullish oscillations are still present but are hidden by the distorting
feedback actions of the Fed. Then, the antibubble signature could be better
observed from the different reference frame of foreigners.

Figure 2 shows the S&P 500 index denominated in EUR from 2000/08/09 to
2004/04/16 and its fits using the first-order and second-order Landau formulas.
Recall that we have shown a similar figure in our update on 2003/10/20.

Figure 3 shows the S&P 500 index denominated in GBP from 2000/08/09 to
2004/04/16 and its fits using the first-order and second-order Landau formulas.

Figure 4 shows the S&P 500 index denominated in XAU from 2000/08/09 to
2004/04/16 and its fits using the first-order and second-order Landau formulas.

Figure 5 shows the r.m.s. (root-mean-square, a measure of the quality of the
fits) of the fit residuals of the retrospective fits, such as those shown in
Figs. 2-4. This figure shows very clearly the change of regime around February
2003, materialized by the jump in r.m.s. in ALL fits. Note that the same occurs
for the S&P 500 in US dollar. It is also very interesting to see that the
first-order fit and the second-order fit separate around Feb 2003, that is,
there is a bifurcation in the data (the bifurcation is slightly earlier for
AU). It is also clear from the figure that there is another change of regime
around the beginning of 2004. Beyond the quality and predictive power of the
proposed fits, we would like to stress the importance of identifying "regime
switches".

Several of our readers suggested that we should also investigate the stock
indexes in the Europe since those are traded directly in EUR and in GBP. We
thus show below the counterparts of the S&P 500 in EUR and in GBP with
DAX of Germany, CAC 40 of France, and FTSE of the United Kingdom. We see that
the antibubble is right on track in these stock markets.

Figure 6 shows the DAX of Germany from 2000/08/09 to 2004/04/16 and its fits
using the first-order and second-order Landau formulas.

Figure 7 shows the CAC 40 of France from 2000/08/09 to 2004/04/16 and its
fits using the first-order and second-order Landau formulas.

Figure 8 shows the FTSE of the United Kingdom from 2000/08/09 to 2004/04/16
and its fits using the first-order and second-order Landau formulas.

THIS IS AN EXPERIMENT PERFORMED IN REAL TIME AND WE WILL CONTINUE UPDATING
EVERY MONTH.

REMEMBER THAT this analysis is for academic purposes only and must
not be construed as investment or trading advice.